Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space
Geometric Topology
2026-03-10 v2 Group Theory
Metric Geometry
Abstract
We prove that convex-cocompact representations of finitely generated groups in the group of isometries of the infinite-dimensional hyperbolic space form an open set in the space of representations, allowing us to deform these convex-cocompact representations. We then use bending to obtain convex-cocompact representations of surface groups that are not conjugate to any exotic representation of PSL(2,R) classified by Monod and Py.
Keywords
Cite
@article{arxiv.2402.12294,
title = {Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space},
author = {David Xu},
journal= {arXiv preprint arXiv:2402.12294},
year = {2026}
}
Comments
An error was found in the proof of the main theorem in the previous version. The argument has been revised accordingly, and the present version proves a weaker form of the main theorem